Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 8, 12, 16, 20, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 4
- d = 12 − 8 = 4
- Tₙ = a + (n − 1)d = 8 + (n − 1) × 4 = 4n + 4
2.Find the sum of the first 6 terms of the geometric sequence −1, −2, −4, −8, …
Answer: −63
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (26 − 1) ÷ (2 − 1)
- = −63
3.For the arithmetic sequence 18, 19, 20, 21, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 17
- d = 19 − 18 = 1
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 1 = n + 17
4.For the arithmetic sequence 9, 17, 25, 33, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 1
- d = 17 − 9 = 8
- Tₙ = a + (n − 1)d = 9 + (n − 1) × 8 = 8n + 1
5.Find the sum of the first 5 terms of the geometric sequence −1, −2, −4, −8, …
Answer: −31
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (25 − 1) ÷ (2 − 1)
- = −31
6.For the arithmetic sequence 1, 9, 17, 25, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 7
- d = 9 − 1 = 8
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 8 = 8n − 7
7.Find the sum of the first 26 terms of the arithmetic sequence 1, −1, −3, −5, …
Answer: −624
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 1 + 25 × −2)
- = −624
8.Find the 19th term of the arithmetic sequence −6, −10, −14, −18, …
Answer: −78
- a = −6, d = −4
- T19 = −6 + 18 × −4 = −78
9.Find the sum of the first 5 terms of the geometric sequence −4, −8, −16, −32, …
Answer: −124
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (25 − 1) ÷ (2 − 1)
- = −124
10.For the arithmetic sequence −1, 5, 11, 17, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 7
- d = 5 − (−1) = 6
- Tₙ = a + (n − 1)d = −1 + (n − 1) × 6 = 6n − 7
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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